I could previously run phantomjs (phantomjs.org) using a shell_exec command in PHP, however I am no longer able to using Dreamhost hosting.

On goDaddy I was able to download, extract & run the Linux version of phantomjs (phantomjs-1.8.1-linux-x86_64.tar.bz2) from phantomjs.org. I copied the resulting file structure to my hosting account where I could run phantomjs using the PHP code, e.g.

The results you’re showing from running “file” differ from what I got, and suggest very strongly that it’s the 32-bit version. (In particular, the “ELF 32-bit LSB executable” bit.) Can you please try redownloading the 64-bit version? If that doesn’t work, email me with your shell username and I’ll take a look.